79,329 research outputs found
Answer Set Planning Under Action Costs
Recently, planning based on answer set programming has been proposed as an
approach towards realizing declarative planning systems. In this paper, we
present the language Kc, which extends the declarative planning language K by
action costs. Kc provides the notion of admissible and optimal plans, which are
plans whose overall action costs are within a given limit resp. minimum over
all plans (i.e., cheapest plans). As we demonstrate, this novel language allows
for expressing some nontrivial planning tasks in a declarative way.
Furthermore, it can be utilized for representing planning problems under other
optimality criteria, such as computing ``shortest'' plans (with the least
number of steps), and refinement combinations of cheapest and fastest plans. We
study complexity aspects of the language Kc and provide a transformation to
logic programs, such that planning problems are solved via answer set
programming. Furthermore, we report experimental results on selected problems.
Our experience is encouraging that answer set planning may be a valuable
approach to expressive planning systems in which intricate planning problems
can be naturally specified and solved
Robust Algorithms for TSP and Steiner Tree
Robust optimization is a widely studied area in operations research, where
the algorithm takes as input a range of values and outputs a single solution
that performs well for the entire range. Specifically, a robust algorithm aims
to minimize regret, defined as the maximum difference between the solution's
cost and that of an optimal solution in hindsight once the input has been
realized. For graph problems in P, such as shortest path and minimum spanning
tree, robust polynomial-time algorithms that obtain a constant approximation on
regret are known. In this paper, we study robust algorithms for minimizing
regret in NP-hard graph optimization problems, and give constant approximations
on regret for the classical traveling salesman and Steiner tree problems.Comment: 39 pages. An extended abstract of this paper appeared in the
Proceedings of the 47th International Colloquium on Automata, Languages, and
Programming (ICALP), 202
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Social Equity Impacts of Congestion Management Strategies
This white paper examines the social equity impacts of various congestion management strategies. The paper includes a comprehensive list of 30 congestion management strategies and a discussion of equity implications related to each strategy. The authors analyze existing literature and incorporate findings from 12 expert interviews from academic, non-governmental organization (NGO), public, and private sector respondents to strengthen results and fill gaps in understanding. The literature review applies the Spatial – Temporal – Economic – Physiological – Social (STEPS) Equity Framework (Shaheen et al., 2017) to identify impacts and classify whether social equity barriers are reduced, exacerbated, or both by a particular congestion mitigation measure. The congestion management strategies discussed are grouped into six main categories, including: 1) pricing, 2) parking and curb policies, 3) operational strategies, 4) infrastructure changes, 5) transportation services and strategies, and 6) conventional taxation. The findings show that the social equity impacts of certain congestion management strategies are not well understood, at present, and further empirical research is needed. Congestion mitigation measures have the potential to affect travel costs, commute times, housing, and accessibility in ways that are distinctly positive or negative for different populations. For these reasons, social equity implications of congestion management strategies should be understood and mitigated for in planning and implementation of these strategies
Translation from Classical Two-Way Automata to Pebble Two-Way Automata
We study the relation between the standard two-way automata and more powerful
devices, namely, two-way finite automata with an additional "pebble" movable
along the input tape. Similarly as in the case of the classical two-way
machines, it is not known whether there exists a polynomial trade-off, in the
number of states, between the nondeterministic and deterministic pebble two-way
automata. However, we show that these two machine models are not independent:
if there exists a polynomial trade-off for the classical two-way automata, then
there must also exist a polynomial trade-off for the pebble two-way automata.
Thus, we have an upward collapse (or a downward separation) from the classical
two-way automata to more powerful pebble automata, still staying within the
class of regular languages. The same upward collapse holds for complementation
of nondeterministic two-way machines.
These results are obtained by showing that each pebble machine can be, by
using suitable inputs, simulated by a classical two-way automaton with a linear
number of states (and vice versa), despite the existing exponential blow-up
between the classical and pebble two-way machines
The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme
The Traveling Salesman Problem (TSP) is among the most famous NP-hard
optimization problems. We design for this problem a randomized polynomial-time
algorithm that computes a (1+eps)-approximation to the optimal tour, for any
fixed eps>0, in TSP instances that form an arbitrary metric space with bounded
intrinsic dimension.
The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the
above result holds in the special case of TSP in a fixed-dimensional Euclidean
space. Thus, our algorithm demonstrates that the algorithmic tractability of
metric TSP depends on the dimensionality of the space and not on its specific
geometry. This result resolves a problem that has been open since the
quasi-polynomial time algorithm of Talwar (T-04)
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